Tatius, legendary king of the Sabines and co-regent at Rome for 5 years with Romulus, is used by two moneyers in the Republic as an obverse type. Tatius appear in some of the earliest Latin literature in a famously alliterative line of Ennius:
What a mouthful!
The translations too often depend on what people think the context is:
Warmington in the Loeb clearly assumes a negative context (above). This reading has been endorsed again by a recent introductory essay on Ennius. [Not bad little introduction to his alliterative tendencies there too.] By contrast Elliott very recently has swung out to an opposite positive direction:
I rather like this more neutral rendering (It is widely quoted thus (an example), I’ve not bothered tracking down who the original translator is):
O Titus Tatius, Tyrant, what great things you have brought upon yourself!
Reading Ennius as having a negative portrayal of Tatius makes it more difficult to explain his presence on coins. The desire to commemorate him on the state coinage pre-supposes a positive legacy.
The coin, I suppose, evokes something closer to the sentiments of this line of Propertius:
qui quaerit Tatium veterem durosque Sabinos,
hic posuit nostra nuper in urbe pedem.
Propertius says chaste and modest girls might existed in the past but that’s not how this are now or appear to be in the various mythological allusions.
It seems that Tatius has a reputation (along with his fellow sabines) as a guarantor of moral rectitude, perhaps an allusion to his (their) punishment of Tarpeia?
For smart things about Sabines on Coins, see Farney.